Models and least squares

The following exercises will help you understand linear models and how to solve for model parameters. The exercises focus on:

projections and their use in fitting linear models to data.
on affine transformations
polynomial model.

Please prioritize your time accordingly, where your priority should be given to the first two exercises. The tasks related polynomial models will be revisited in later weeks.

Linear models are extremely important for understanding machine learning models in general. Therefore, we highly recommend that you use every possible opportunity to ask for help if you have trouble understanding any of the concepts. The exercise about learning an affine 2D transformation is important for solving the assignment next week, so please make sure that you complete each task with a high priority.

Learning goals

After this week's exercises, you should be able to:

Reason about the relationship between projections and least squares.
Learn and apply an affine transformation.
Estimate and visualize the transformed points.
Reflect upon the possibilites and limitations of linear least squares.
Train, compare and reason about the performance of polynomial models.